则运
Kó
2017 10 16
Kó
则运
1
2
3 则运
4
5
Kó
则运
1
2
3 则运
4
5
Kó
则运
1
2
3 则运
4
5
Kó
则运
1
2
3 则运
4
5
Kó
则运
1
2
3 则运
4
5
Kó
则运
1 (ëÖ8)
OØMichael SiperÍÅ
OØÄ:LewisÍuÆ
gÄÅØóÚOØJ.E.HopcroftÍ[
Å
/ªógÄÅkÍÅ
Kó
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µ
: £
Neither Front Rear Both
Closed Closed Open Closed Closed
Open Closed Open Open Open
Kó
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µ
: £
Neither Front Rear Both
Closed Closed Open Closed Closed
Open Closed Open Open Open
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Front
Rear!Both!Neither
Neither
Front!Rear!Both
Kó
则运
Â
q
1
start
q
2
q
3
0
1
1
0
0, 1
L(M) =
{ω|ω11
0}
T
1101, 1010
AMN
§¡AM
§L(M ) = A"¡
M/A
M§
仍然§
Kó
则运
Â
q
1
start
q
2
q
3
0
1
1
0
0, 1
L(M) =
{ω|ω11
0}
T
1101, 1010
AMN
§¡AM
§L(M ) = A"¡
M/A
M§
仍然§
Kó
则运
Â
q
1
start
q
2
q
3
0
1
1
0
0, 1
L(M) =
{ω|ω11
0}
T
1101, 1010
AMN
§¡AM
§L(M ) = A"¡
M/A
M§
仍然§
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则运
Â
q
1
start
q
2
q
3
0
1
1
0
0, 1
L(M) =
{ω|ω11
0}
T
1101, 1010
AMN
§¡AM
§L(M ) = A"¡
M/A
M§
仍然§
Kó
则运
Â
q
1
start
q
2
q
3
0
1
1
0
0, 1
L(M) =
{ω|ω11
0}
T
1101, 1010
AMN
§¡AM
§L(M ) = A"¡
M/A
M§
仍然§
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则运
Â
q
1
start
q
2
q
3
0
1
1
0
0, 1
L(M) =
{ω|ω11
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T
1101, 1010
AMN
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P
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µ
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P
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q
0
Q
F Q
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2 (ÄM = ({q
1
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}, {0, 1}, δ, q
1
, {q
2
}))
q
1
start
q
2
0
1
1
0
M´Ä´£O011011, 100110
L(M) =
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2 (ÄM = ({q
1
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2
}, {0, 1}, δ, q
1
, {q
2
}))
q
1
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q
2
0
1
1
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M´Ä´£O011011, 100110
L(M) =
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Kó
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2 (ÄM = ({q
1
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2
}, {0, 1}, δ, q
1
, {q
2
}))
q
1
start
q
2
0
1
1
0
M´Ä´£O011011, 100110
L(M) =
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2 (ÄM = ({q
1
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2
}, {0, 1}, δ, q
1
, {q
2
}))
q
1
start
q
2
0
1
1
0
M´Ä´£O011011, 100110
L(M) =
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Kó
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Þ~
2 (ÄM = ({q
1
, q
2
}, {0, 1}, δ, q
1
, {q
2
}))
q
1
start
q
2
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1
1
0
M´Ä´£O011011, 100110
L(M) ={ω|ω1å}
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3 (ÄM = ({q
1
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1
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1
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q
1
start
q
2
0
1
1
0
M´Ä´£O011011, 100110
duå©G´ÉGdGε L(M)
L(M) =
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Kó
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3 (ÄM = ({q
1
, q
2
}, {0, 1}, δ, q
1
, {q
1
}))
q
1
start
q
2
0
1
1
0
M´Ä´£O011011, 100110
duå©G´ÉGdGε L(M)
L(M) =
{ω|ω = ε½0å}
Kó
则运
Þ~
3 (ÄM = ({q
1
, q
2
}, {0, 1}, δ, q
1
, {q
1
}))
q
1
start
q
2
0
1
1
0
M´Ä´£O011011, 100110
duå©G´ÉGdGε L(M)
L(M) =
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Kó
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3 (ÄM = ({q
1
, q
2
}, {0, 1}, δ, q
1
, {q
1
}))
q
1
start
q
2
0
1
1
0
M´Ä´£O011011, 100110
duå©G´ÉGdGε L(M)
L(M) =
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Kó
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Þ~
3 (ÄM = ({q
1
, q
2
}, {0, 1}, δ, q
1
, {q
1
}))
q
1
start
q
2
0
1
1
0
M´Ä´£O011011, 100110
duå©G´ÉGdGε L(M)
L(M) =
{ω|ω = ε½0å}
Kó
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Þ~
3 (ÄM = ({q
1
, q
2
}, {0, 1}, δ, q
1
, {q
1
}))
q
1
start
q
2
0
1
1
0
M´Ä´£O011011, 100110
duå©G´ÉGdGε L(M)
L(M) ={ω|ω = ε½0å}
Kó
则运
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M = (Q,
P
, δ, q
0
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, i = 0, 1, · · · , n 1
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n
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0
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1
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2
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1
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M = (Q,
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F
KMÉw
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则运
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XJA = {w|MÉw}KM £OóA
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start
q
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bi1L´{0, 1}¦EU£ODz´Û
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q
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bi1L´{0, 1}¦EU£ODz´Û
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q
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1
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bi1L´{0, 1}¦EU£ODz´Û
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q
even
start
q
odd
0
1
0
1
Kó
则运
5 (bi1L´{a, b}¦Ä
EL(M) = {ω|ω = a, b½ωå©"iÎ}gÄÅ)
s
start
q
1
r
1
q
2
r
2
a
b
a
b
b
a
b
a
a
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则运
5 (bi1L´{a, b}¦Ä
EL(M) = {ω|ω = a, b½ωå©"iÎ}gÄÅ)
s
start
q
1
r
1
q
2
r
2
a
b
a
b
b
a
b
a
a
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Kó
则运
6 (i1L{0, 1, 2},
EL(M) = {ω|ω½êiÚ´3ê}gÄÅ)
q
0
start
q
1
q
2
0
1
2
0
1
2
0
2
1
Kó
则运
6 (i1L{0, 1, 2},
EL(M) = {ω|ω½êiÚ´3ê}gÄÅ)
q
0
start
q
1
q
2
0
1
2
0
1
2
0
2
1
Kó
则运
7 (E£O{w|x01y, x, y {0, 1}
}gÄÅ)
q
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start
q
2
q
1
0, 1
1
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00
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Kó
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}gÄÅ)
q
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start
q
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q
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0, 1
1
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00
1
Kó
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7 (E£O{w|x01y, x, y {0, 1}
}gÄÅ)
q
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start
q
2
q
1
0, 1
1
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00
1
Kó
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7 (E£O{w|x01y, x, y {0, 1}
}gÄÅ)
q
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start
q
2
q
1
0, 1
1
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1
Kó
则运
7 (E£O{w|x01y, x, y {0, 1}
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q
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start
q
2
q
1
0, 1
1
0
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1
Kó
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}gÄÅ)
q
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start
q
2
q
1
0, 1
1
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Kó
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bi1L´{0, 1}¦EU£O¹iÎ
G001¤kiÎGgÄÅ
q:vk?ÛUy
3001¥ÎÒ;
q
0
:10;
q
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q
001
:fG001;
q
start
q
0
q
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q
001
1
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1
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0, 1
Kó
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bi1L´{0, 1}¦EU£O¹iÎ
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q
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q
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q
start
q
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q
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q
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1
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Kó
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bi1L´{0, 1}¦EU£O¹iÎ
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q
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q
start
q
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q
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q
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1
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Kó
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q
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q
start
q
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q
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q
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1
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Kó
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q
start
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1
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q
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q
start
q
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q
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q
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1
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0
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0, 1
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q
0
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q
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q
start
q
0
q
00
q
001
1
0
0
1
0
1
0, 1
Kó
则运
S1
EL(M) = {ω|ω1m©0å}DFA
EL(M) = {ω|ωÝØu31nÎÒ´0}
EL(M) = {ω|ω´11Ú111?G}
EL(M) = {ε, 0}
Kó
则运
S1
EL(M) = {ω|ω1m©0å}DFA
EL(M) = {ω|ωÝØu31nÎÒ´0}
EL(M) = {ω|ω´11Ú111?G}
EL(M) = {ε, 0}
Kó
则运
S1
EL(M) = {ω|ω1m©0å}DFA
EL(M) = {ω|ωÝØu31nÎÒ´0}
EL(M) = {ω|ω´11Ú111?G}
EL(M) = {ε, 0}
Kó
则运
S1
EL(M) = {ω|ω1m©0å}DFA
EL(M) = {ω|ωÝØu31nÎÒ´0}
EL(M) = {ω|ω´11Ú111?G}
EL(M) = {ε, 0}
Kó
则运
q
1
start
q
2
q
3
q
4
0, 1
1
0, ε
1
0, 1
(DFA)(NFA)µ
DFA£Þ
Ñ
NFA0!1
£ÞÑ
DFA£Þ
NFA£Þ±ε§
ε£Þ
Kó
则运
q
1
start
q
2
q
3
q
4
0, 1
1
0, ε
1
0, 1
(DFA)(NFA)µ
DFA£Þ
Ñ
NFA0!1
£ÞÑ
DFA£Þ
NFA£Þ±ε§
ε£Þ
Kó
则运
q
1
start
q
2
q
3
q
4
0, 1
1
0, ε
1
0, 1
(DFA)(NFA)µ
DFA£Þ
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NFA0!1
£ÞÑ
DFA£Þ
NFA£Þ±ε§
ε£Þ
Kó
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q
1
start
q
2
q
3
q
4
0, 1
1
0, ε
1
0, 1
(DFA)(NFA)µ
DFA£Þ
Ñ
NFA0!1
£ÞÑ
DFA£Þ
NFA£Þ±ε§
ε£Þ
Kó
则运
q
1
start
q
2
q
3
q
4
0, 1
1
0, ε
1
0, 1
(DFA)(NFA)µ
DFA£Þ
Ñ
NFA0!1
£ÞÑ
DFA£Þ
NFA£Þ±ε§
ε£Þ
Kó
则运
q
1
start
q
2
q
3
q
4
0, 1
1
0, ε
1
0, 1
(DFA)(NFA)µ
DFA£Þ
Ñ
NFA0!1
£ÞÑ
DFA£Þ
NFA£Þ±ε§
ε£Þ
Kó
则运
q
1
start
q
2
q
3
q
4
0, 1
1
0, ε
1
0, 1
010110µ
q
1
start
q
1
0
q
1
1
q
2
1
q
3
1
q
1
0
q
3
0
Kó
则运
q
1
start
q
2
q
3
q
4
0, 1
1
0, ε
1
0, 1
010110µ
q
1
start
q
1
0
q
1
1
q
2
1
q
3
1
q
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0
q
3
0
Kó
则运
q
1
start
q
2
q
3
q
4
0, 1
1
0, ε
1
0, 1
010110µ
q
1
start
q
1
0
q
1
1
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2
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q
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q
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3
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Kó
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q
1
start
q
2
q
3
q
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0, 1
1
0, ε
1
0, 1
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q
1
start
q
1
0
q
1
1
q
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q
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q
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Kó
则运
q
1
start
q
2
q
3
q
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0, 1
1
0, ε
1
0, 1
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q
1
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则运
NFAÂ
½5 ((½.k¡gÄÅ(NFA))
NFA´5|(Q,
P
, δ, q
0
, F )Ù¥
Q´k¡G8
P
´k¡i1L
δ : Q ×
P
ε
P(Q)´=¼êÙ¥
X
ε
=
X
∪{ε}
P(Q)´Q8
q
0
Q´å©G
F Q´ÉG8
Kó
则运
NFAÂ
½5 ((½.k¡gÄÅ(NFA))
NFA´5|(Q,
P
, δ, q
0
, F )Ù¥
Q´k¡G8
P
´k¡i1L
δ : Q ×
P
ε
P(Q)´=¼êÙ¥
X
ε
=
X
∪{ε}
P(Q)´Q8
q
0
Q´å©G
F Q´ÉG8
Kó
则运
NFAÂ
½6
N = (Q,
P
, δ, q
0
, F )´NFAw = y
1
y
2
· · · y
m
Ù
¥y
i
P
ε
e3Q¥GSr
0
, r
1
, · · · , r
m
÷v
1 r
0
= q
0
2 r
i+1
δ(r
0
, y
i+1
), i = 0, 1, · · · , m 1
3 r
m
F
KNÉw
Kó
则运
NFAÂ
½6
N = (Q,
P
, δ, q
0
, F )´NFAw = y
1
y
2
· · · y
m
Ù
¥y
i
P
ε
e3Q¥GSr
0
, r
1
, · · · , r
m
÷v
1 r
0
= q
0
2 r
i+1
δ(r
0
, y
i+1
), i = 0, 1, · · · , m 1
3 r
m
F
KNÉw
Kó
则运
NFAÂ
½6
N = (Q,
P
, δ, q
0
, F )´NFAw = y
1
y
2
· · · y
m
Ù
¥y
i
P
ε
e3Q¥GSr
0
, r
1
, · · · , r
m
÷v
1 r
0
= q
0
2 r
i+1
δ(r
0
, y
i+1
), i = 0, 1, · · · , m 1
3 r
m
F
KNÉw
Kó
则运
NFAÂ
½6
N = (Q,
P
, δ, q
0
, F )´NFAw = y
1
y
2
· · · y
m
Ù
¥y
i
P
ε
e3Q¥GSr
0
, r
1
, · · · , r
m
÷v
1 r
0
= q
0
2 r
i+1
δ(r
0
, y
i+1
), i = 0, 1, · · · , m 1
3 r
m
F
KNÉw
Kó
则运
NFAÂ
½6
N = (Q,
P
, δ, q
0
, F )´NFAw = y
1
y
2
· · · y
m
Ù
¥y
i
P
ε
e3Q¥GSr
0
, r
1
, · · · , r
m
÷v
1 r
0
= q
0
2 r
i+1
δ(r
0
, y
i+1
), i = 0, 1, · · · , m 1
3 r
m
F
KNÉw
Kó
则运
NFA!DFA的等
½7 (d)
eÅì£OóK§´d
½1 (NFADFAd5)
z(½5k¡gÄÅ(NFA)Ñdu,(½.
k¡gÄÅ(DFA)
NFA)ε
NFA£§
Kó
则运
NFA!DFA的等
½7 (d)
eÅì£OóK§´d
½1 (NFADFAd5)
z(½5k¡gÄÅ(NFA)Ñdu,(½.
k¡gÄÅ(DFA)
NFA)ε
NFA£§
Kó
则运
NFA!DFA的等
½7 (d)
eÅì£OóK§´d
½1 (NFADFAd5)
z(½5k¡gÄÅ(NFA)Ñdu,(½.
k¡gÄÅ(DFA)
NFA)ε
NFA£§
Kó
则运
NFA!DFA的等
½7 (d)
eÅì£OóK§´d
½1 (NFADFAd5)
z(½5k¡gÄÅ(NFA)Ñdu,(½.
k¡gÄÅ(DFA)
NFA)ε
NFA£§
Kó
则运
NFA!DFA的等
½7 (d)
eÅì£OóK§´d
½1 (NFADFAd5)
z(½5k¡gÄÅ(NFA)Ñdu,(½.
k¡gÄÅ(DFA)
NFA)ε
NFA£§
Kó
则运
NFA!DFA的等
.
N = (Q, Σ, δ, q
0
, F )是识ANFA§DFA
Mµ
µQ
0
= P(Q)
£µ
δ
0
(R, a) = {q Q | r R, q
E(
δ(r, a))}
E(R) = {q|RÑ沿0εÞq}
еq
0
0
= E{q
0
}
µF
0
= {R Q
0
|RN }
Kó
则运
NFA!DFA的等
.
N = (Q, Σ, δ, q
0
, F )是识ANFA§DFA
Mµ
µQ
0
= P(Q)
£µ
δ
0
(R, a) = {q Q | r R, q
E(
δ(r, a))}
E(R) = {q|RÑ沿0εÞq}
еq
0
0
= E{q
0
}
µF
0
= {R Q
0
|RN }
Kó
则运
NFA!DFA的等
.
N = (Q, Σ, δ, q
0
, F )是识ANFA§DFA
Mµ
µQ
0
= P(Q)
£µ
δ
0
(R, a) = {q Q | r R, q
E(
δ(r, a))}
E(R) = {q|RÑ沿0εÞq}
еq
0
0
= E{q
0
}
µF
0
= {R Q
0
|RN }
Kó
则运
NFA!DFA的等
.
N = (Q, Σ, δ, q
0
, F )是识ANFA§DFA
Mµ
µQ
0
= P(Q)
£µ
δ
0
(R, a) = {q Q | r R, q E(δ(r, a))}
E(R) = {q|RÑ沿0εÞq}
еq
0
0
= E{q
0
}
µF
0
= {R Q
0
|RN }
Kó
则运
NFA!DFA的等
.
N = (Q, Σ, δ, q
0
, F )是识ANFA§DFA
Mµ
µQ
0
= P(Q)
£µ
δ
0
(R, a) = {q Q | r R, q E(δ(r, a))}
E(R) = {q|RÑ沿0εÞq}
еq
0
0
= E{q
0
}
µF
0
= {R Q
0
|RN }
Kó
则运
NFA!DFA的等
.
N = (Q, Σ, δ, q
0
, F )是识ANFA§DFA
Mµ
µQ
0
= P(Q)
£µ
δ
0
(R, a) = {q Q | r R, q E(δ(r, a))}
E(R) = {q|RÑ沿0εÞq}
еq
0
0
= E{q
0
}
µF
0
= {R Q
0
|RN }
Kó
则运
NFA!DFA的等
14 (NFADFA=)
NXe¤«NFA
1
start
2 3
b
ε
a
a, b
a
¦dDFA
Kó
则运
NFA!DFA的等
{1} {2} {1, 2}
{3} {1, 3} {2, 3} {1, 2, 3}
a, b
a
b
a
b
a, b
a
b
a
b
a
b
a
b
Kó
则运
NFA!DFA的等
{1} {2} {1, 2}
{3} {1, 3} {2, 3} {1, 2, 3}
a, b
a
b
a
b
a, b
a
b
a
b
a
b
a
b
Kó
则运
NFA!DFA的等
{1} {2} {1, 2}
{3} {1, 3} {2, 3} {1, 2, 3}
a, b
a
b
a
b
a, b
a
b
a
b
a
b
a
b
Kó
则运
NFA!DFA的等
{1} {2} {1, 2}
{3} {1, 3} {2, 3} {1, 2, 3}
a, b
a
b
a
b
a, b
a
b
a
b
a
b
a
b
Kó
则运
NFA!DFA的等
{1} {2} {1, 2}
{3} {1, 3} {2, 3} {1, 2, 3}
a, b
a
b
a
b
a, b
a
b
a
b
a
b
a
b
Kó
则运
NFA!DFA的等
{1} {2} {1, 2}
{3} {1, 3} {2, 3} {1, 2, 3}
a, b
a
b
a
b
a, b
a
b
a
b
a
b
a
b
Kó
则运
NFA!DFA的等
{1} {2} {1, 2}
{3} {1, 3} {2, 3} {1, 2, 3}
a, b
a
b
a
b
a, b
a
b
a
b
a
b
a
b
Kó
则运
NFA!DFA的等
{1} {2} {1, 2}
{3} {1, 3} {2, 3} {1, 2, 3}
a, b
a
b
a
b
a, b
a
b
a
b
a
b
a
b
Kó
则运
NFA!DFA的等
{1} {2} {1, 2}
{3} {1, 3} {2, 3} {1, 2, 3}
a, b
a
b
a
b
a, b
a
b
a
b
a
b
a
b
Kó
则运
NFA!DFA的等
{1, 3}
start
{3}
{2} {2, 3} {1, 2, 3}
a
b
a
b
a, b
b
a
a
b
Kó
则运
则运
½8 (K$)
A, B´ó½K$
¿A B = {x|x A ½ x B}
A B = {xy|x A y B}
(ÒA
= {x
1
x
2
· · · x
k
|k 0zx
i
A}
¿µÃA是什§ε A
"
Aµ
={ε}"
Kó
则运
则运
½8 (K$)
A, B´ó½K$
¿A B = {x|x A ½ x B}
A B = {xy|x A y B}
(ÒA
= {x
1
x
2
· · · x
k
|k 0zx
i
A}
¿µÃA是什§ε A
"
Aµ
={ε}"
Kó
则运
则运
½8 (K$)
A, B´ó½K$
¿A B = {x|x A ½ x B}
A B = {xy|x A y B}
(ÒA
= {x
1
x
2
· · · x
k
|k 0zx
i
A}
¿µÃA是什§ε A
"
Aµ
={ε}"
Kó
则运
则运
½8 (K$)
A, B´ó½K$
¿A B = {x|x A ½ x B}
A B = {xy|x A y B}
(ÒA
= {x
1
x
2
· · · x
k
|k 0zx
i
A}
¿µÃA是什§ε A
"
Aµ
={ε}"
Kó
则运
则运
½8 (K$)
A, B´ó½K$
¿A B = {x|x A ½ x B}
A B = {xy|x A y B}
(ÒA
= {x
1
x
2
· · · x
k
|k 0zx
i
A}
¿µÃA是什§ε A
"
Aµ
={ε}"
Kó
则运
则运
½8 (K$)
A, B´ó½K$
¿A B = {x|x A ½ x B}
A B = {xy|x A y B}
(ÒA
= {x
1
x
2
· · · x
k
|k 0zx
i
A}
¿µÃA是什§ε A
"
Aµ
=
{ε}"
Kó
则运
则运
½8 (K$)
A, B´ó½K$
¿A B = {x|x A ½ x B}
A B = {xy|x A y B}
(ÒA
= {x
1
x
2
· · · x
k
|k 0zx
i
A}
¿µÃA是什§ε A
"
Aµ
={ε}"
Kó
则运
½2 (Kóµ45)
Kó3¿$eµ4
Kó3$eµ4
Kó3(Ò$eµ4
Kó3Öeµ4
Kó3eµ4
Kó
则运
½2 (Kóµ45)
Kó3¿$eµ4
Kó3$eµ4
Kó3(Ò$eµ4
Kó3Öeµ4
Kó3eµ4
Kó
则运
½2 (Kóµ45)
Kó3¿$eµ4
Kó3$eµ4
Kó3(Ò$eµ4
Kó3Öeµ4
Kó3eµ4
Kó
则运
½2 (Kóµ45)
Kó3¿$eµ4
Kó3$eµ4
Kó3(Ò$eµ4
Kó3Öeµ4
Kó3eµ4
Kó
则运
½2 (Kóµ45)
Kó3¿$eµ4
Kó3$eµ4
Kó3(Ò$eµ4
Kó3Öeµ4
Kó3eµ4
Kó
则运
½3 (Kó3¿
$eµ4)
DFA M
1
, M
2
A
1
, A
2
§
M
i
= (Q
i
, Σ, δ
i
, q
i
, F
i
), i { 0, 1}
A
1
A
2
DFA M µ
Q = Q
1
× Q
2
;
Σ
0
= Σ;
δ((r
1
, r
2
), a) = {δ
1
(r
1
, a), δ
2
(r
2
, a)}
q
0
= (q
1
, q
2
)
F = {(r
1
, r
2
) | (r
1
F
1
) (r
2
F
2
)}
{(r
1
, r
2
) | (r
1
F
1
) (r
2
F
2
)}
Kó
则运
½3 (Kó3¿
$eµ4)
DFA M
1
, M
2
A
1
, A
2
§
M
i
= (Q
i
, Σ, δ
i
, q
i
, F
i
), i { 0, 1}
A
1
A
2
DFA M µ
Q = Q
1
× Q
2
;
Σ
0
= Σ;
δ((r
1
, r
2
), a) = {δ
1
(r
1
, a), δ
2
(r
2
, a)}
q
0
= (q
1
, q
2
)
F = {(r
1
, r
2
) | (r
1
F
1
) (r
2
F
2
)}
{(r
1
, r
2
) | (r
1
F
1
) (r
2
F
2
)}
Kó
则运
½3 (Kó3¿
$eµ4)
DFA M
1
, M
2
A
1
, A
2
§
M
i
= (Q
i
, Σ, δ
i
, q
i
, F
i
), i { 0, 1}
A
1
A
2
DFA M µ
Q = Q
1
× Q
2
;
Σ
0
= Σ;
δ((r
1
, r
2
), a) = {δ
1
(r
1
, a), δ
2
(r
2
, a)}
q
0
= (q
1
, q
2
)
F = {(r
1
, r
2
) | (r
1
F
1
) (r
2
F
2
)}
{(r
1
, r
2
) | (r
1
F
1
) (r
2
F
2
)}
Kó
则运
½3 (Kó3¿
$eµ4)
DFA M
1
, M
2
A
1
, A
2
§
M
i
= (Q
i
, Σ, δ
i
, q
i
, F
i
), i { 0, 1}
A
1
A
2
DFA M µ
Q = Q
1
× Q
2
;
Σ
0
= Σ;
δ((r
1
, r
2
), a) = {δ
1
(r
1
, a), δ
2
(r
2
, a)}
q
0
= (q
1
, q
2
)
F = {(r
1
, r
2
) | (r
1
F
1
) (r
2
F
2
)}
{(r
1
, r
2
) | (r
1
F
1
) (r
2
F
2
)}
Kó
则运
½3 (Kó3¿
$eµ4)
DFA M
1
, M
2
A
1
, A
2
§
M
i
= (Q
i
, Σ, δ
i
, q
i
, F
i
), i { 0, 1}
A
1
A
2
DFA M µ
Q = Q
1
× Q
2
;
Σ
0
= Σ;
δ((r
1
, r
2
), a) = {δ
1
(r
1
, a), δ
2
(r
2
, a)}
q
0
= (q
1
, q
2
)
F = {(r
1
, r
2
) | (r
1
F
1
) (r
2
F
2
)}
{(r
1
, r
2
) | (r
1
F
1
) (r
2
F
2
)}
Kó
则运
½3 (Kó3¿
$eµ4)
DFA M
1
, M
2
A
1
, A
2
§
M
i
= (Q
i
, Σ, δ
i
, q
i
, F
i
), i { 0, 1}
A
1
A
2
DFA M µ
Q = Q
1
× Q
2
;
Σ
0
= Σ;
δ((r
1
, r
2
), a) = {δ
1
(r
1
, a), δ
2
(r
2
, a)}
q
0
= (q
1
, q
2
)
F = {(r
1
, r
2
) | (r
1
F
1
) (r
2
F
2
)}
{(r
1
, r
2
) | (r
1
F
1
) (r
2
F
2
)}
Kó
则运
½3 (Kó3¿
$eµ4)
DFA M
1
, M
2
A
1
, A
2
§
M
i
= (Q
i
, Σ, δ
i
, q
i
, F
i
), i { 0, 1}
A
1
A
2
DFA M µ
Q = Q
1
× Q
2
;
Σ
0
= Σ;
δ((r
1
, r
2
), a) = {δ
1
(r
1
, a), δ
2
(r
2
, a)}
q
0
= (q
1
, q
2
)
F = {(r
1
, r
2
) | (r
1
F
1
) (r
2
F
2
)}
{(r
1
, r
2
) | (r
1
F
1
) (r
2
F
2
)}
Kó
则运
½3 (Kó3¿$eµ4)
DFA M
1
, M
2
A
1
, A
2
§
M
i
= (Q
i
, Σ, δ
i
, q
i
, F
i
), i { 0, 1}
A
1
A
2
DFA M µ
Q = Q
1
× Q
2
;
Σ
0
= Σ;
δ((r
1
, r
2
), a) = {δ
1
(r
1
, a), δ
2
(r
2
, a)}
q
0
= (q
1
, q
2
)
F = {(r
1
, r
2
) | (r
1
F
1
) (r
2
F
2
)}
{(r
1
, r
2
) | (r
1
F
1
) (r
2
F
2
)}
Kó
则运
½3 (Kó3¿$eµ4)
DFA M
1
, M
2
A
1
, A
2
§
M
i
= (Q
i
, Σ, δ
i
, q
i
, F
i
), i { 0, 1}
A
1
A
2
DFA M µ
Q = Q
1
× Q
2
;
Σ
0
= Σ;
δ((r
1
, r
2
), a) = {δ
1
(r
1
, a), δ
2
(r
2
, a)}
q
0
= (q
1
, q
2
)
F = {(r
1
, r
2
) | (r
1
F
1
) (r
2
F
2
)}{(r
1
, r
2
) | (r
1
F
1
) (r
2
F
2
)}
Kó
则运
½4 (“Kó3¿$eµ4”)
NFA, DFA的等
Q = {q
0
} Q
1
Q
2
δ(q, a) =
δ
1
(q, a) q Q
1
δ
2
(q, a) q Q
2
{q
1
, q
2
} q = q
0
, a = ε
q = q
0
, a 6= ε
F = F
1
F
2
Kó
则运
½4 (“Kó3¿$eµ4”)
NFA, DFA的等
Q = {q
0
} Q
1
Q
2
δ(q, a) =
δ
1
(q, a) q Q
1
δ
2
(q, a) q Q
2
{q
1
, q
2
} q = q
0
, a = ε
q = q
0
, a 6= ε
F = F
1
F
2
Kó
则运
½4 (“Kó3¿$eµ4”)
NFA, DFA的等
Q = {q
0
} Q
1
Q
2
δ(q, a) =
δ
1
(q, a) q Q
1
δ
2
(q, a) q Q
2
{q
1
, q
2
} q = q
0
, a = ε
q = q
0
, a 6= ε
F = F
1
F
2
Kó
则运
½5 (“Kó3$eµ4”)
Q = Q
1
Q
2
q
1
δ(q, a) =
δ
1
(q, a) q Q
1
, q 6∈ F
1
δ
1
(q, a) q F
1
, a 6= ε
δ
1
(q, a) {q
2
} q F
1
, a = ε
δ
2
(q, a) q Q
2
F = F
2
Kó
则运
½5 (“Kó3$eµ4”)
Q = Q
1
Q
2
q
1
δ(q, a) =
δ
1
(q, a) q Q
1
, q 6∈ F
1
δ
1
(q, a) q F
1
, a 6= ε
δ
1
(q, a) {q
2
} q F
1
, a = ε
δ
2
(q, a) q Q
2
F = F
2
Kó
则运
½5 (“Kó3$eµ4”)
Q = Q
1
Q
2
q
1
δ(q, a) =
δ
1
(q, a) q Q
1
, q 6∈ F
1
δ
1
(q, a) q F
1
, a 6= ε
δ
1
(q, a) {q
2
} q F
1
, a = ε
δ
2
(q, a) q Q
2
F = F
2
Kó
则运
½5 (“Kó3$eµ4”)
Q = Q
1
Q
2
q
1
δ(q, a) =
δ
1
(q, a) q Q
1
, q 6∈ F
1
δ
1
(q, a) q F
1
, a 6= ε
δ
1
(q, a) {q
2
} q F
1
, a = ε
δ
2
(q, a) q Q
2
F = F
2
Kó
则运
½6 (“Kó3(Ò$eµ4”)
Q = {q
0
} Q
1
q
0
δ(q, a) =
δ
1
(q, a) q Q
1
, q 6∈ F
1
δ
1
(q, a) q F
1
, a 6= ε
δ
1
(q, a) {q
1
} q F
1
, a = ε
{q
1
} q = q
0
, a = ε
q = q
0
, a 6= ε
F = {q
0
} F
2
Kó
则运
½6 (“Kó3(Ò$eµ4”)
Q = {q
0
} Q
1
q
0
δ(q, a) =
δ
1
(q, a) q Q
1
, q 6∈ F
1
δ
1
(q, a) q F
1
, a 6= ε
δ
1
(q, a) {q
1
} q F
1
, a = ε
{q
1
} q = q
0
, a = ε
q = q
0
, a 6= ε
F = {q
0
} F
2
Kó
则运
½6 (“Kó3(Ò$eµ4”)
Q = {q
0
} Q
1
q
0
δ(q, a) =
δ
1
(q, a) q Q
1
, q 6∈ F
1
δ
1
(q, a) q F
1
, a 6= ε
δ
1
(q, a) {q
1
} q F
1
, a = ε
{q
1
} q = q
0
, a = ε
q = q
0
, a 6= ε
F = {q
0
} F
2
Kó
则运
½6 (“Kó3(Ò$eµ4”)
Q = {q
0
} Q
1
q
0
δ(q, a) =
δ
1
(q, a) q Q
1
, q 6∈ F
1
δ
1
(q, a) q F
1
, a 6= ε
δ
1
(q, a) {q
1
} q F
1
, a = ε
{q
1
} q = q
0
, a = ε
q = q
0
, a 6= ε
F = {q
0
} F
2
Kó
则运
½9 (KLª)
U^K$ÎE£ãóLª
(0 1)0
d0½1¡?0¤kiÎG|
ó
(0 1)
d0, 1¤kiÎG|ó
P
´?i1LK
KLª
P
L«i1Lþ¤kÝ1iÎG¤|
ó;
P
L«i1Lþ¤kiÎG|ó
3KLª¥`kgS´(Ò¿
Kó
则运
½9 (KLª)
U^K$ÎE£ãóLª
(0 1)0
d0½1¡?0¤kiÎG|
ó
(0 1)
d0, 1¤kiÎG|ó
P
´?i1LK
KLª
P
L«i1Lþ¤kÝ1iÎG¤|
ó;
P
L«i1Lþ¤kiÎG|ó
3KLª¥`kgS´(Ò¿
Kó
则运
½9 (KLª)
U^K$ÎE£ãóLª
(0 1)0
d0½1¡?0¤kiÎG|
ó
(0 1)
d0, 1¤kiÎG|ó
P
´?i1LK
KLª
P
L«i1Lþ¤kÝ1iÎG¤|
ó;
P
L«i1Lþ¤kiÎG|ó
3KLª¥`kgS´(Ò¿
Kó
则运
½9 (KLª)
U^K$ÎE£ãóLª
(0 1)0
d0½1¡?0¤kiÎG|
ó
(0 1)
d0, 1¤kiÎG|ó
P
´?i1LK
KLª
P
L«i1Lþ¤kÝ1iÎG¤|
ó;
P
L«i1Lþ¤kiÎG|ó
3KLª¥`kgS´(Ò¿
Kó
则运
½9 (KLª)
U^K$ÎE£ãóLª
(0 1)0
d0½1¡?0¤kiÎG|
ó
(0 1)
d0, 1¤kiÎG|ó
P
´?i1LK
KLª
P
L«i1Lþ¤kÝ1iÎG¤|
ó;
P
L«i1Lþ¤kiÎG|ó
3KLª¥`kgS´(Ò¿
Kó
则运
½9 (KLª)
U^K$ÎE£ãóLª
(0 1)0
d0½1¡?0¤kiÎG|
ó
(0 1)
d0, 1¤kiÎG|ó
P
´?i1LK
KLª
P
L«i1Lþ¤kÝ1iÎG¤|
ó;
P
L«i1Lþ¤kiÎG|ó
3KLª¥`kgS´(Ò¿
Kó
则运
½9 (KLª)
U^K$ÎE£ãóLª
(0 1)0
d0½1¡?0¤kiÎG|
ó
(0 1)
d0, 1¤kiÎG|ó
P
´?i1LK
KLª
P
L«i1Lþ¤kÝ1iÎG¤|
ó;
P
L«i1Lþ¤kiÎG|ó
3KLª¥`kgS´(Ò¿
Kó
则运
½9 (KLª)
U^K$ÎE£ãóLª
(0 1)0
d0½1¡?0¤kiÎG|
ó
(0 1)
d0, 1¤kiÎG|ó
P
´?i1LK
KLª
P
L«i1Lþ¤kÝ1iÎG¤|
ó;
P
L«i1Lþ¤kiÎG|ó
3KLª¥`kgS´(Ò¿
Kó
则运
½9 (KLª)
U^K$ÎE£ãóLª
(0 1)0
d0½1¡?0¤kiÎG|
ó
(0 1)
d0, 1¤kiÎG|ó
P
´?i1LK
KLª
P
L«i1Lþ¤kÝ1iÎG¤|
ó;
P
L«i1Lþ¤kiÎG|ó
3KLª¥`kgS´(Ò¿
Kó
则运
½9 (KLª)
U^K$ÎE£ãóLª
(0 1)0
d0½1¡?0¤kiÎG|
ó
(0 1)
d0, 1¤kiÎG|ó
P
´?i1LK
KLª
P
L«i1Lþ¤kÝ1iÎG¤|
ó;
P
L«i1Lþ¤kiÎG|ó
3KLª¥`kgS´(Ò¿
Kó
则运
Â
½10 (KLª)
R´KLªXJR´
1 {a}({Pa)Ù¥a
P
=ó{a}
2 ε=ó{ε}
3 =ع?ÛiÎGó-ó
4 (R
1
R
2
)
5 (R
1
R
2
)
6 (R
1
)
Ù¥R
1
, R
2
´KLª
A§R
+
= RR
§Rë(¤"
Kó
则运
Â
½10 (KLª)
R´KLªXJR´
1 {a}({Pa)Ù¥a
P
=ó{a}
2 ε=ó{ε}
3 =ع?ÛiÎGó-ó
4 (R
1
R
2
)
5 (R
1
R
2
)
6 (R
1
)
Ù¥R
1
, R
2
´KLª
A§R
+
= RR
§Rë(¤"
Kó
则运
Â
½10 (KLª)
R´KLªXJR´
1 {a}({Pa)Ù¥a
P
=ó{a}
2 ε=ó{ε}
3 =ع?ÛiÎGó-ó
4 (R
1
R
2
)
5 (R
1
R
2
)
6 (R
1
)
Ù¥R
1
, R
2
´KLª
A§R
+
= RR
§Rë(¤"
Kó
则运
Â
15 (i1L
P
= {0, 1})
0
10
=
{ω|ω¥Tk1}
P
1
P
=
{ω|ω¥k1}
(01
+
)
=
{ω|ω¥z0¡1}
(
PP
)
=
{ω|ω´ÝóêiÎG}
0
P
0 1
P
1 0 1 =
{ω|ω¥ÎÒ}
(0 ε)(1 ε) =
{ε, 0, 1, 01}
1
=
=
{ε}
Kó
则运
Â
15 (i1L
P
= {0, 1})
0
10
={ω|ω¥Tk1}
P
1
P
=
{ω|ω¥k1}
(01
+
)
=
{ω|ω¥z0¡1}
(
PP
)
=
{ω|ω´ÝóêiÎG}
0
P
0 1
P
1 0 1 =
{ω|ω¥ÎÒ}
(0 ε)(1 ε) =
{ε, 0, 1, 01}
1
=
=
{ε}
Kó
则运
Â
15 (i1L
P
= {0, 1})
0
10
={ω|ω¥Tk1}
P
1
P
={ω|ω¥k1}
(01
+
)
=
{ω|ω¥z0¡1}
(
PP
)
=
{ω|ω´ÝóêiÎG}
0
P
0 1
P
1 0 1 =
{ω|ω¥ÎÒ}
(0 ε)(1 ε) =
{ε, 0, 1, 01}
1
=
=
{ε}
Kó
则运
Â
15 (i1L
P
= {0, 1})
0
10
={ω|ω¥Tk1}
P
1
P
={ω|ω¥k1}
(01
+
)
={ω|ω¥z0¡1}
(
PP
)
=
{ω|ω´ÝóêiÎG}
0
P
0 1
P
1 0 1 =
{ω|ω¥ÎÒ}
(0 ε)(1 ε) =
{ε, 0, 1, 01}
1
=
=
{ε}
Kó
则运
Â
15 (i1L
P
= {0, 1})
0
10
={ω|ω¥Tk1}
P
1
P
={ω|ω¥k1}
(01
+
)
={ω|ω¥z0¡1}
(
PP
)
={ω|ω´ÝóêiÎG}
0
P
0 1
P
1 0 1 =
{ω|ω¥ÎÒ}
(0 ε)(1 ε) =
{ε, 0, 1, 01}
1
=
=
{ε}
Kó
则运
Â
15 (i1L
P
= {0, 1})
0
10
={ω|ω¥Tk1}
P
1
P
={ω|ω¥k1}
(01
+
)
={ω|ω¥z0¡1}
(
PP
)
={ω|ω´ÝóêiÎG}
0
P
0 1
P
1 0 1 ={ω|ω¥ÎÒ}
(0 ε)(1 ε) =
{ε, 0, 1, 01}
1
=
=
{ε}
Kó
则运
Â
15 (i1L
P
= {0, 1})
0
10
={ω|ω¥Tk1}
P
1
P
={ω|ω¥k1}
(01
+
)
={ω|ω¥z0¡1}
(
PP
)
={ω|ω´ÝóêiÎG}
0
P
0 1
P
1 0 1 ={ω|ω¥ÎÒ}
(0 ε)(1 ε) ={ε, 0, 1, 01}
1
=
=
{ε}
Kó
则运
Â
15 (i1L
P
= {0, 1})
0
10
={ω|ω¥Tk1}
P
1
P
={ω|ω¥k1}
(01
+
)
={ω|ω¥z0¡1}
(
PP
)
={ω|ω´ÝóêiÎG}
0
P
0 1
P
1 0 1 ={ω|ω¥ÎÒ}
(0 ε)(1 ε) ={ε, 0, 1, 01}
1
=
=
{ε}
Kó
则运
Â
15 (i1L
P
= {0, 1})
0
10
={ω|ω¥Tk1}
P
1
P
={ω|ω¥k1}
(01
+
)
={ω|ω¥z0¡1}
(
PP
)
={ω|ω´ÝóêiÎG}
0
P
0 1
P
1 0 1 ={ω|ω¥ÎÒ}
(0 ε)(1 ε) ={ε, 0, 1, 01}
1
=
={ε}
Kó
则运
与有的等
½7 (ó´K´Ù^KL
ª\£ã)
16 (òKLª(a b)
aba=zNFA)
a
start
a
Kó
则运
与有的等
½7 (ó´K´Ù^KL
ª\£ã)
16 (òKLª(a b)
aba=zNFA)
a
start
a
Kó
则运
与有的等
½7 (ó´K´Ù^KL
ª\£ã)
16 (òKLª(a b)
aba=zNFA)
a
start
a
Kó
则运
与有的等
½7 (ó´K´Ù^KL
ª\£ã)
16 (òKLª(a b)
aba=zNFA)
a
start
a
Kó
则运
与有的等
a b
start
ε
a
ε
b
Kó
则运
与有的等
a b
start
ε
a
ε
b
Kó
则运
与有的等
(a b)
start
ε
a
ε
b
ε
ε
ε
Kó
则运
与有的等
(a b)
start
ε
a
ε
b
ε
ε
ε
Kó
则运
与有的等
a
ba
:
start
a ε b ε a
Kó
则运
与有的等
a
ba
:
start
a
ε b ε a
Kó
则运
与有的等
ab
a
:
start
a
ε b ε a
Kó
则运
与有的等
ab
a
:
start
a ε b
ε a
Kó
则运
与有的等
aba:
start
a ε b
ε a
Kó
则运
与有的等
aba:
start
a ε b ε a
Kó
则运
与有的等
(a b)
aba:
Kó
则运
与有的等
½11 (2(½.k¡gÄÅ(GNFA))
?ÛKLªIÒNFA2(½.
k¡gÄÅ(GNFA)=ÙIÒØ´i1L¥½ε
AGNFA:
Þ§
Þ
§Þ§
ÑÞ§Ó
Ø!§!
Þ
Kó
则运
与有的等
½11 (2(½.k¡gÄÅ(GNFA))
?ÛKLªIÒNFA2(½.
k¡gÄÅ(GNFA)=ÙIÒØ´i1L¥½ε
AGNFA:
Þ§
Þ
§Þ§
ÑÞ§Ó
Ø!§!
Þ
Kó
则运
与有的等
½11 (2(½.k¡gÄÅ(GNFA))
?ÛKLªIÒNFA2(½.
k¡gÄÅ(GNFA)=ÙIÒØ´i1L¥½ε
AGNFA:
Þ§
Þ
§Þ§
ÑÞ§Ó
Ø!§!
Þ
Kó
则运
与有的等
½11 (2(½.k¡gÄÅ(GNFA))
?ÛKLªIÒNFA2(½.
k¡gÄÅ(GNFA)=ÙIÒØ´i1L¥½ε
AGNFA:
Þ§
Þ
§Þ§
ÑÞ§Ó
Ø!§!
Þ
Kó
则运
与有的等
½11 (2(½.k¡gÄÅ(GNFA))
?ÛKLªIÒNFA2(½.
k¡gÄÅ(GNFA)=ÙIÒØ´i1L¥½ε
AGNFA:
Þ§
Þ
§Þ§
ÑÞ§Ó
Ø!§!
Þ
Kó
则运
与有的等
DFA(A)GNFAµ
V§使
εÞ
εÞ
ü向相ÓÞ§O
±Þ
ÞVÞ
Kó
则运
与有的等
DFA(A)GNFAµ
V§使
εÞ
εÞ
ü向相ÓÞ§O
±Þ
ÞVÞ
Kó
则运
与有的等
DFA(A)GNFAµ
V§使
εÞ
εÞ
ü向相ÓÞ§O
±Þ
ÞVÞ
Kó
则运
与有的等
DFA(A)GNFAµ
V§使
εÞ
εÞ
ü向相ÓÞ§O
±Þ
ÞVÞ
Kó
则运
与有的等
DFA(A)GNFAµ
V§使
εÞ
εÞ
ü向相ÓÞ§O
±Þ
ÞVÞ
Kó
则运
与有的等
DFA(A)GNFAµ
V§使
εÞ
εÞ
ü向相ÓÞ§O
±Þ
ÞVÞ
Kó
则运
与有的等
1
start
2
a
b
a, b
s
start
1
a
2
ε
a
b
a b
ε
Kó
则运
与有的等
1
start
2
a
b
a, b
s
start
1
a
2
ε
a
b
a b
ε
Kó
则运
与有的等
s
start
1
a
2
ε
a
b
a b
ε
Kó
则运
与有的等
s
start
1
a
2
ε
a
b
a b
ε
Kó
则运
与有的等
s
start
1
a
2
ε
a
b
a b
ε
Kó
则运
与有的等
s
start
1
a
2
ε
a
b
a b
ε
Kó
则运
与有的等
صØq
del
§
q
i
q
del
R
1
Þ
q
del
R
2
Þ;
q
del
q
j
R
3
Þ;
q
i
q
j
R
4
Þ
q
i
q
j
Þ
(R
1
)(R
2
)
(R
3
) (R
4
)
Kó
则运
与有的等
صØq
del
§
q
i
q
del
R
1
Þ
q
del
R
2
Þ;
q
del
q
j
R
3
Þ;
q
i
q
j
R
4
Þ
q
i
q
j
Þ
(R
1
)(R
2
)
(R
3
) (R
4
)
Kó
则运
与有的等
صØq
del
§
q
i
q
del
R
1
Þ
q
del
R
2
Þ;
q
del
q
j
R
3
Þ;
q
i
q
j
R
4
Þ
q
i
q
j
Þ
(R
1
)(R
2
)
(R
3
) (R
4
)
Kó
则运
与有的等
صØq
del
§
q
i
q
del
R
1
Þ
q
del
R
2
Þ;
q
del
q
j
R
3
Þ;
q
i
q
j
R
4
Þ
q
i
q
j
Þ
(R
1
)(R
2
)
(R
3
) (R
4
)
Kó
则运
与有的等
صØq
del
§
q
i
q
del
R
1
Þ
q
del
R
2
Þ;
q
del
q
j
R
3
Þ;
q
i
q
j
R
4
Þ
q
i
q
j
Þ
(R
1
)(R
2
)
(R
3
) (R
4
)
Kó
则运
与有的等
صØq
del
§
q
i
q
del
R
1
Þ
q
del
R
2
Þ;
q
del
q
j
R
3
Þ;
q
i
q
j
R
4
Þ
q
i
q
j
Þ
(R
1
)(R
2
)
(R
3
) (R
4
)
Kó
则运
与有的等
s
start
1
a
2
ε
a
b
a b
ε
s
start
1
a
ε
a
b(a b)
Kó
则运
与有的等
s
start
1
a
2
ε
a
b
a b
ε
s
start
1
a
ε
a
b(a b)
Kó
则运
与有的等
s
start
1
a
2
ε
a
b
a b
ε
s
start
1
a
ε
a
b(a b)
Kó
则运
与有的等
s
start
1
a
ε
a
b(a b)
s
start
a
a
b(a b)
Kó
则运
与有的等
s
start
1
a
ε
a
b(a b)
s
start
a
a
b(a b)
Kó
则运
与有的等
s
start
1
a
ε
a
b(a b)
s
start
a
a
b(a b)
Kó
则运
与有的等
17 ((½eDFAéAKLª)
1
start
2
3
a
b
b
a
b
a
Kó
则运
与有的等
s
start
1 2
3
a
a
b
b
a
b
a
ε ε
ε
Kó
则运
与有的等
s
start
2
3
a
E
1
E
2
E
3
E
4
E
5
E
6
E
7
E
8
E
1
: a
E
2
: b
E
3
: aa b
E
4
: ab
E
5
: ε
E
6
: bb
E
7
: ba a
E
8
: ε
Kó
则运
与有的等
s
start
2
3
a
E
1
E
2
E
3
E
4
E
5
E
6
E
7
E
8
E
1
: a
E
2
: b
E
3
: aa b
E
4
: ab
E
5
: ε
E
6
: bb
E
7
: ba a
E
8
: ε
Kó
则运
与有的等
s
start
3
a
E
1
E
2
E
3
E
4
E
1
: a(aa b)
E
2
: a(aa b)
ab b
E
3
: (ba a)(aa b)
ab bb
E
4
: (ba a)(aa b)
ε
Kó
则运
与有的等
s
start
3
a
E
1
E
2
E
3
E
4
E
1
: a(aa b)
E
2
: a(aa b)
ab b
E
3
: (ba a)(aa b)
ab bb
E
4
: (ba a)(aa b)
ε
Kó
则运
与有的等
s
start
a
E
E : (a(aa b)
ab b)((ba a)(aa b)
ab bb)
((ba
a)(aa b)
) (a(aa b)
)
Kó
则运
与有的等
s
start
a
E
E : (a(aa b)
ab b)((ba a)(aa b)
ab bb)
((ba
a)(aa b)
) (a(aa b)
)
Kó
则运
½8 (")
eA´KóK3êp¦XJs´A¥?
ÝØupiÎGKs©3ã=s = xyz
÷v
1 ézi 0kxy
i
z A
2 |y| > 0
3 |xy| p
p"Ý
Kó
则运
½8 (")
eA´KóK3êp¦XJs´A¥?
ÝØupiÎGKs©3ã=s = xyz
÷v
1 ézi 0kxy
i
z A
2 |y| > 0
3 |xy| p
p"Ý
Kó
则运
½8 (")
eA´KóK3êp¦XJs´A¥?
ÝØupiÎGKs©3ã=s = xyz
÷v
1 ézi 0kxy
i
z A
2 |y| > 0
3 |xy| p
p"Ý
Kó
则运
½8 (")
eA´KóK3êp¦XJs´A¥?
ÝØupiÎGKs©3ã=s = xyz
÷v
1 ézi 0kxy
i
z A
2 |y| > 0
3 |xy| p
p"Ý
Kó
则运
½8 (")
eA´KóK3êp¦XJs´A¥?
ÝØupiÎGKs©3ã=s = xyz
÷v
1 ézi 0kxy
i
z A
2 |y| > 0
3 |xy| p
p"Ý
Kó
则运
½8 (")
eA´KóK3êp¦XJs´A¥?
ÝØupiÎGKs©3ã=s = xyz
÷v
1 ézi 0kxy
i
z A
2 |y| > 0
3 |xy| p
p"Ý
Kó
则运
18 (y²B = {0
n
1
n
|n 0}Ø´Kó)
y
bB´Kp´ÙA"Ý ÄiÎ
Gs = 0
p
1
p
Bs = xyz3"e©ãK
ey = 0
t
, 0 < t < pK
xyyz 6∈ B
ey = 1
t
, 0 < t < pK
xyyz 6∈ B
ey = 0
t
1
1
t
2
, t
1
, t
2
> 0K
xyyz 6∈ B
Kó
则运
18 (y²B = {0
n
1
n
|n 0}Ø´Kó)
y bB´Kp´ÙA"Ý
ÄiÎ
Gs = 0
p
1
p
Bs = xyz3"e©ãK
ey = 0
t
, 0 < t < pK
xyyz 6∈ B
ey = 1
t
, 0 < t < pK
xyyz 6∈ B
ey = 0
t
1
1
t
2
, t
1
, t
2
> 0K
xyyz 6∈ B
Kó
则运
18 (y²B = {0
n
1
n
|n 0}Ø´Kó)
y bB´Kp´ÙA"Ý ÄiÎ
Gs = 0
p
1
p
Bs = xyz3"e©ãK
ey = 0
t
, 0 < t < pK
xyyz 6∈ B
ey = 1
t
, 0 < t < pK
xyyz 6∈ B
ey = 0
t
1
1
t
2
, t
1
, t
2
> 0K
xyyz 6∈ B
Kó
则运
18 (y²B = {0
n
1
n
|n 0}Ø´Kó)
y bB´Kp´ÙA"Ý ÄiÎ
Gs = 0
p
1
p
Bs = xyz3"e©ãK
ey = 0
t
, 0 < t < pK
xyyz 6∈ B
ey = 1
t
, 0 < t < pK
xyyz 6∈ B
ey = 0
t
1
1
t
2
, t
1
, t
2
> 0K
xyyz 6∈ B
Kó
则运
18 (y²B = {0
n
1
n
|n 0}Ø´Kó)
y bB´Kp´ÙA"Ý ÄiÎ
Gs = 0
p
1
p
Bs = xyz3"e©ãK
ey = 0
t
, 0 < t < pKxyyz 6∈ B
ey = 1
t
, 0 < t < pK
xyyz 6∈ B
ey = 0
t
1
1
t
2
, t
1
, t
2
> 0K
xyyz 6∈ B
Kó
则运
18 (y²B = {0
n
1
n
|n 0}Ø´Kó)
y bB´Kp´ÙA"Ý ÄiÎ
Gs = 0
p
1
p
Bs = xyz3"e©ãK
ey = 0
t
, 0 < t < pKxyyz 6∈ B
ey = 1
t
, 0 < t < pK
xyyz 6∈ B
ey = 0
t
1
1
t
2
, t
1
, t
2
> 0K
xyyz 6∈ B
Kó
则运
18 (y²B = {0
n
1
n
|n 0}Ø´Kó)
y bB´Kp´ÙA"Ý ÄiÎ
Gs = 0
p
1
p
Bs = xyz3"e©ãK
ey = 0
t
, 0 < t < pKxyyz 6∈ B
ey = 1
t
, 0 < t < pKxyyz 6∈ B
ey = 0
t
1
1
t
2
, t
1
, t
2
> 0K
xyyz 6∈ B
Kó
则运
18 (y²B = {0
n
1
n
|n 0}Ø´Kó)
y bB´Kp´ÙA"Ý ÄiÎ
Gs = 0
p
1
p
Bs = xyz3"e©ãK
ey = 0
t
, 0 < t < pKxyyz 6∈ B
ey = 1
t
, 0 < t < pKxyyz 6∈ B
ey = 0
t
1
1
t
2
, t
1
, t
2
> 0K
xyyz 6∈ B
Kó
则运
18 (y²B = {0
n
1
n
|n 0}Ø´Kó)
y bB´Kp´ÙA"Ý ÄiÎ
Gs = 0
p
1
p
Bs = xyz3"e©ãK
ey = 0
t
, 0 < t < pKxyyz 6∈ B
ey = 1
t
, 0 < t < pKxyyz 6∈ B
ey = 0
t
1
1
t
2
, t
1
, t
2
> 0Kxyyz 6∈ B
Kó
则运
19 (y²B = {w|w¥0, 1ê}Ø´Kó)
y
bB´Kp´ÙA"Ý ÄiÎ
Gs = 0
p
1
p
Bs = xyz3"e©ãK
du|xy| pdy = 0
t
, 0 < t p
xyyz 6∈ B
Kó
则运
19 (y²B = {w|w¥0, 1ê}Ø´Kó)
y bB´Kp´ÙA"Ý
ÄiÎ
Gs = 0
p
1
p
Bs = xyz3"e©ãK
du|xy| pdy = 0
t
, 0 < t p
xyyz 6∈ B
Kó
则运
19 (y²B = {w|w¥0, 1ê}Ø´Kó)
y bB´Kp´ÙA"Ý ÄiÎ
Gs = 0
p
1
p
Bs = xyz3"e©ãK
du|xy| pdy = 0
t
, 0 < t p
xyyz 6∈ B
Kó
则运
19 (y²B = {w|w¥0, 1ê}Ø´Kó)
y bB´Kp´ÙA"Ý ÄiÎ
Gs = 0
p
1
p
Bs = xyz3"e©ãK
du|xy| pdy = 0
t
, 0 < t p
xyyz 6∈ B
Kó
则运
19 (y²B = {w|w¥0, 1ê}Ø´Kó)
y bB´Kp´ÙA"Ý ÄiÎ
Gs = 0
p
1
p
Bs = xyz3"e©ãK
du|xy| pdy = 0
t
, 0 < t p
xyyz 6∈ B
Kó
则运
20 (y²C = {ww|w {0, 1}
}Ø´Kó)
y
bC´Kp´ÙA"Ý ÄiÎ
Gs = 0
p
10
p
1 Cs = xyz3"e©ãK
du|xy| p, |y| > 0K
y = 0
t
, t p
ddxyyz 6∈ C
21 (y²D = {0
i
1
j
|i > j}Ø´Kó)
y
bD´Kp´ÙA"Ý ÄiÎ
Gs = 0
p+1
1
p
Ds = xyz3"e©ãK
du|xy| p, |y| > 0Ky = 0
t
, 0 < t p
ddxy
0
z = xz 6∈ D
Kó
则运
20 (y²C = {ww|w {0, 1}
}Ø´Kó)
y bC´Kp´ÙA"Ý
ÄiÎ
Gs = 0
p
10
p
1 Cs = xyz3"e©ãK
du|xy| p, |y| > 0K
y = 0
t
, t p
ddxyyz 6∈ C
21 (y²D = {0
i
1
j
|i > j}Ø´Kó)
y
bD´Kp´ÙA"Ý ÄiÎ
Gs = 0
p+1
1
p
Ds = xyz3"e©ãK
du|xy| p, |y| > 0Ky = 0
t
, 0 < t p
ddxy
0
z = xz 6∈ D
Kó
则运
20 (y²C = {ww|w {0, 1}
}Ø´Kó)
y bC´Kp´ÙA"Ý ÄiÎ
Gs = 0
p
10
p
1 Cs = xyz3"e©ãK
du|xy| p, |y| > 0K
y = 0
t
, t p
ddxyyz 6∈ C
21 (y²D = {0
i
1
j
|i > j}Ø´Kó)
y
bD´Kp´ÙA"Ý ÄiÎ
Gs = 0
p+1
1
p
Ds = xyz3"e©ãK
du|xy| p, |y| > 0Ky = 0
t
, 0 < t p
ddxy
0
z = xz 6∈ D
Kó
则运
20 (y²C = {ww|w {0, 1}
}Ø´Kó)
y bC´Kp´ÙA"Ý ÄiÎ
Gs = 0
p
10
p
1 Cs = xyz3"e©ãK
du|xy| p, |y| > 0K
y = 0
t
, t p
ddxyyz 6∈ C
21 (y²D = {0
i
1
j
|i > j}Ø´Kó)
y
bD´Kp´ÙA"Ý ÄiÎ
Gs = 0
p+1
1
p
Ds = xyz3"e©ãK
du|xy| p, |y| > 0Ky = 0
t
, 0 < t p
ddxy
0
z = xz 6∈ D
Kó
则运
20 (y²C = {ww|w {0, 1}
}Ø´Kó)
y bC´Kp´ÙA"Ý ÄiÎ
Gs = 0
p
10
p
1 Cs = xyz3"e©ãK
du|xy| p, |y| > 0Ky = 0
t
, t p
ddxyyz 6∈ C
21 (y²D = {0
i
1
j
|i > j}Ø´Kó)
y
bD´Kp´ÙA"Ý ÄiÎ
Gs = 0
p+1
1
p
Ds = xyz3"e©ãK
du|xy| p, |y| > 0Ky = 0
t
, 0 < t p
ddxy
0
z = xz 6∈ D
Kó
则运
20 (y²C = {ww|w {0, 1}
}Ø´Kó)
y bC´Kp´ÙA"Ý ÄiÎ
Gs = 0
p
10
p
1 Cs = xyz3"e©ãK
du|xy| p, |y| > 0Ky = 0
t
, t p
ddxyyz 6∈ C
21 (y²D = {0
i
1
j
|i > j}Ø´Kó)
y
bD´Kp´ÙA"Ý ÄiÎ
Gs = 0
p+1
1
p
Ds = xyz3"e©ãK
du|xy| p, |y| > 0Ky = 0
t
, 0 < t p
ddxy
0
z = xz 6∈ D
Kó
则运
20 (y²C = {ww|w {0, 1}
}Ø´Kó)
y bC´Kp´ÙA"Ý ÄiÎ
Gs = 0
p
10
p
1 Cs = xyz3"e©ãK
du|xy| p, |y| > 0Ky = 0
t
, t p
ddxyyz 6∈ C
21 (y²D = {0
i
1
j
|i > j}Ø´Kó)
y bD´Kp´ÙA"Ý
ÄiÎ
Gs = 0
p+1
1
p
Ds = xyz3"e©ãK
du|xy| p, |y| > 0Ky = 0
t
, 0 < t p
ddxy
0
z = xz 6∈ D
Kó
则运
20 (y²C = {ww|w {0, 1}
}Ø´Kó)
y bC´Kp´ÙA"Ý ÄiÎ
Gs = 0
p
10
p
1 Cs = xyz3"e©ãK
du|xy| p, |y| > 0Ky = 0
t
, t p
ddxyyz 6∈ C
21 (y²D = {0
i
1
j
|i > j}Ø´Kó)
y bD´Kp´ÙA"Ý ÄiÎ
Gs = 0
p+1
1
p
Ds = xyz3"e©ãK
du|xy| p, |y| > 0Ky = 0
t
, 0 < t p
ddxy
0
z = xz 6∈ D
Kó
则运
20 (y²C = {ww|w {0, 1}
}Ø´Kó)
y bC´Kp´ÙA"Ý ÄiÎ
Gs = 0
p
10
p
1 Cs = xyz3"e©ãK
du|xy| p, |y| > 0Ky = 0
t
, t p
ddxyyz 6∈ C
21 (y²D = {0
i
1
j
|i > j}Ø´Kó)
y bD´Kp´ÙA"Ý ÄiÎ
Gs = 0
p+1
1
p
Ds = xyz3"e©ãK
du|xy| p, |y| > 0Kxyyx
?
6∈ D
du|xy| p, |y| > 0
Ky = 0
t
, 0 < t p
ddxy
0
z = xz 6∈ D
Kó
则运
20 (y²C = {ww|w {0, 1}
}Ø´Kó)
y bC´Kp´ÙA"Ý ÄiÎ
Gs = 0
p
10
p
1 Cs = xyz3"e©ãK
du|xy| p, |y| > 0Ky = 0
t
, t p
ddxyyz 6∈ C
21 (y²D = {0
i
1
j
|i > j}Ø´Kó)
y bD´Kp´ÙA"Ý ÄiÎ
Gs = 0
p+1
1
p
Ds = xyz3"e©ãK
du|xy| p, |y| > 0Ky = 0
t
, 0 < t p
ddxy
0
z = xz 6∈ D
Kó
则运
20 (y²C = {ww|w {0, 1}
}Ø´Kó)
y bC´Kp´ÙA"Ý ÄiÎ
Gs = 0
p
10
p
1 Cs = xyz3"e©ãK
du|xy| p, |y| > 0Ky = 0
t
, t p
ddxyyz 6∈ C
21 (y²D = {0
i
1
j
|i > j}Ø´Kó)
y bD´Kp´ÙA"Ý ÄiÎ
Gs = 0
p+1
1
p
Ds = xyz3"e©ãK
du|xy| p, |y| > 0Ky = 0
t
, 0 < t p
ddxy
0
z = xz 6∈ D
Kó